Median spaces have nice embeddings into L^1. Embeddings into L^1 are useful e.g. in computer science, as then one gets access to good algorithms. In 2006 Cheeger and Kleiner showed that the integer Heisenberg group does not bi-Lipschitz embed into L^1. This talk will discuss some of this background as a warm-up for Robert Young's talk(s) later in the semester where he discusses his recent breakthrough with Assaf Naor showing that the (5-dimensional) Heisenberg group fails to embed into L^1 in essentially the worst possible way.